1. Field of the Invention
The present invention relates to a roller bearing which uses cylindrical-shaped, conical-shaped or spherical-shaped rollers as its rolling elements.
2. Description of the Related Art
Now, FIG. 16 shows a state of contact between two cylindrical-shaped elements. Conventionally, there are known various kinds of mechanical elements using this state of rolling contact, such as a roller bearing. On the other hand, this state of rolling contact raises a possibility that, in two end portions of the contact portion in an X-axis direction between the two cylindrical-shaped elements, there can be generated an excessively large contact stress, that is, a so-called edge load. It is also known that such edge load gives rise to the shortened lives of the mechanical elements. In view of this, in a roller bearing, as shown in FIG. 17, a rolling element or a rolling surface is subjected to a crowning so as to gradually reduce the contact stress at the two end portions of the contact portion.
The crowning itself is a known technique. For example, as disclosed in Japanese Utility Model Unexamined Publication No. Hei. 05-89943, there is known an invention which relates to a crowning. Also, referring to the profile of the crowning, there is well known a so called logarithmic crowning which can be expressed by the following equation (1) (A paper titled xe2x80x9cRoller bearings under radial and eccentric loadsxe2x80x9d written by P. M. Johns and R. Gohar, published by TRIBOLOGY International, Vol. 14, 1981, pages 131-136).                     δ        =                              -                          w                              π                ⁢                                  xe2x80x83                                ⁢                                  L                  e                                                              ⁢                      (                                                            1                  -                                      v                    1                    2                                                                    E                  1                                            +                                                1                  -                                      v                    2                    2                                                                    E                  2                                                      )                    ⁢                      In            ⁡                          (                              1                -                                                      (                                          1                      -                                              0.3033                        ⁢                                                                              2                            ⁢                            b                                                                                L                            e                                                                                                                )                                    ⁢                                                            (                                                                        2                          ⁢                          x                                                                          L                          e                                                                    )                                        2                                                              )                                                          (        1        )            
where,
xcex4: sum of crowning quantities of two contact elements (a roller and a raceway surface of an inner race)
w: contact load
Le: effective contact length in a bus extending direction between two contact elements
E1, E2: Young""s modulus of two contact elements (the roller and the inner race)
xcexd1, xcexd2: Poisson""s ratios of two contact elements (the roller and the inner race), and
b: xc2xd of Hertz contact width.
In fact, it is difficult to apply this logarithmic crowning. Therefore, there is a crowning technique which, as disclosed in Japanese Utility Model Unexamined Publication No. Hei. 03-12015, uses a combination of two or more arcs. Also there are proposed crowning techniques which are composed of a single arc, and a combination of a straight line and an arcs. Further, there is known a so-called partial crowning technique in which crownings are subjected only onto the two end portions of the contact surface of a roller or a rolling surface.
According to the above-mentioned crowning techniques, as shown by a two-dot chained line in FIG. 18, preferably, with respect to the effective contact length Le in the bus extending direction, a contact stress may be large in the central portion of the contact portion and gradually decrease in the two end portions of the contact portion. On the other hand, of course, it is not desirable that there is produced an edge load due to the excessively small crowning as shown by line A in FIG. 18. Further, it is not desirable that in case where the crowning reduction quantity is increased excessively due to the excessively large crowning as shown by line B in FIG. 18, the actual contact length of the bus runs short, which gives rise to the shortened life of the roller bearing.
In the above-mentioned logarithmic crowning according to the equation (1), by assuming a contact load w, the crowning profile can be determined. In case where the assumed contact load w is coincident with a load in an actual operation time, the long life of the roller bearing can be expected. However, in case where the two loads are not coincident with other, the long life cannot be expected. Also, for mechanical elements in practical use, it is rare that a load to be applied to the mechanical elements is constant. Inmost cases, various levels of loads are actually applied to the mechanical elements during operation. Further, in a bearing which is used practically, there is a case where a misalignment can occur when assembling the bearing, that is, the misalignment can occur between a center line of a rolling element and a center line of a raceway of an inner race. In that case, the rolling element and the raceway of the inner race are contacted with each other in an inclined manner. Therefore, even in case where the above-mentioned logarithmic crowning has been subjected to the roller or rolling surface, there is still raised a possibility that an edge load can occur on one side end face of the roller or rolling surface to thereby give rise to the shortened life of the bearing. This shows that the above-mentioned logarithmic crowning according to the equation (1) cannot always attain the extended life of the roller bearing.
On the other hand, in the crowning profiles according to the above-mentioned crowning techniques respectively using a single arc, a combination of two or more arcs, and a combination of a straight line and arcs, there have not yet been made the concrete and clear numerical values that can contribute toward extending the life of the roller bearing.
The present invention aims at eliminating the above-mentioned drawbacks found in the conventional roller bearing. Accordingly, it is an object of the invention to provide a roller bearing in which the numerical values of crowning profiles respectively according to concrete combinations of arcs and the numerical values of a partial crowning profile can be made clear to thereby be able to extend the life of the roller bearing.
The object can be achieved by a roller bearing which comprises: a first race having a first raceway; a second race having a second raceway; and a rolling element provided rotatably between the first raceway and the second raceway. In the roller bearing, the sum xcex4 of a crowning quantity of the rolling element and at least a crowning quantity of a first raceway surface of the first raceway, at a first point X1 and a second point X2, wherein the first point X1 is positioned apart from a center of the rolling element or the first raceway in a bus extending direction of a bus of the rolling element by 0.425 Le, and the second point X2 is positioned apart from the center in the bus extending direction by 0.5 Le, where Le denotes an effective contact length in the bus extending direction between the first raceway surface of the first raceway and the rolling surface of the rolling element, satisfies follow equations (1) and (2):
at the first point X1                                                                                                              -                                                                  3.264                        ⁢                        C                                                                                              π                          ·                                                      L                            e                                                    ·                                                      E                            xe2x80x2                                                    ·                          Z                          ·                          cos                                                ⁢                                                  xe2x80x83                                                ⁢                        α                                                                              ⁢                                      In                    ⁡                                          (                                              0.2775                        +                                                  1.583                          xc3x97                                                                                                                    R                                ·                                C                                                                                                                              π                                  ·                                                                      E                                    xe2x80x2                                                                    ·                                                                      L                                    e                                    3                                                                    ·                                  Z                                  ·                                  cos                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                α                                                                                                                                                        )                                                                      ≤                                                    ⁢                                                            δ                ≤                                                      -                                                                  4.896                        ⁢                        C                                                                                              π                          ·                                                      L                            e                                                    ·                                                      E                            xe2x80x2                                                    ·                          Z                          ·                          cos                                                ⁢                                                  xe2x80x83                                                ⁢                        α                                                                              ⁢                                      In                    ⁡                                          (                                              0.2775                        +                                                  1.939                          xc3x97                                                                                                                    R                                ·                                C                                                                                                                              π                                  ·                                                                      E                                    xe2x80x2                                                                    ·                                                                      L                                    e                                    3                                                                    ·                                  Z                                  ·                                  cos                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                α                                                                                                                                                        )                                                                                                                              (2-1)            
and, at the second point X2                                                                                                              -                                                                  3.264                        ⁢                        C                                                                                              π                          ·                                                      L                            e                                                    ·                                                      E                            xe2x80x2                                                    ·                          Z                          ·                          cos                                                ⁢                                                  xe2x80x83                                                ⁢                        α                                                                              ⁢                                      In                    ⁡                                          (                                              2.192                        xc3x97                                                                                                            R                              ·                              C                                                                                                                      π                                ·                                                                  E                                  xe2x80x2                                                                ·                                                                  L                                  e                                  3                                                                ·                                Z                                ·                                cos                                                            ⁢                                                              xe2x80x83                                                            ⁢                              α                                                                                                                          )                                                                      ≤                                                    ⁢                                                            δ                ≤                                                      -                                                                  4.896                        ⁢                        C                                                                                              π                          ·                                                      L                            e                                                    ·                                                      E                            xe2x80x2                                                    ·                          Z                          ·                          cos                                                ⁢                                                  xe2x80x83                                                ⁢                        α                                                                              ⁢                                      In                    ⁡                                          (                                              2.684                        xc3x97                                                                                                            R                              ·                              C                                                                                                                      π                                ·                                                                  E                                  xe2x80x2                                                                ·                                                                  L                                  e                                  3                                                                ·                                Z                                ·                                cos                                                            ⁢                                                              xe2x80x83                                                            ⁢                              α                                                                                                                          )                                                                                                                              (2-2)            
xe2x80x83where,
Exe2x80x2: equivalent modulus of elasticity;
2/Exe2x80x2=(1xe2x88x92xcexd12)/E1+(1xe2x88x92xcexd12)/E2
xe2x80x83E1, E2: Young""s modulus of the rolling element and the first race,
xcexd1, xcexd2: Poisson""s ratios of the rolling element and the first race;
R: equivalent radius
R=r1xc2x7r2/(r1+r2)
xe2x80x83r1: average of radius of the rolling element or average radius of the rolling element
r2: radius of the first raceway at a contact point with a center of the rolling element;
C: basic load rating;
Z: number of rolling elements;
xcex1: contact angle between the first race and the rolling element.
In the above-mentioned roller bearing of the invention, the reason why the distance from the above-mentioned center is specified to be 0.425 Le and 0. 5 Le, that is, the first point X1, and the second point X2 are respectively specified to be positioned apart from the center by 0.425 Le, and 0.5 Le is as follows. That is, although the logarithmic crowning profile theoretically shows the long life of the roller bearing, it is difficult to manufacture such crowning profile. However, the inventors have paid attention to the following fact: that is, in the arc crowning as well, in case where it is set so as to provide a crowning profile approximate to the crowning profile of the logarithmic crowning, the roller bearing can secure a long life. Further, referring to the distance from the center of the roller, the edge load is small around the central portion of the roller but t he edge load increases gradually toward the end portions of the roller. With this characteristic of the edge load taken into account, in a curved line which is obtained by connecting together a plurality of arcs, in case where the crowning reduction quantities at two points on the bus of the roller are specified, a crowning profile can b e defined roughly. As a result of the analysis of the distance, it has been found that, when at the positions where the distances from the center of the roller are 0.425 Le and 0.5 Le on the bus of the roller the crowning profile is included within the range of a proper logarithmic crowning profile, the life of the roller bearing can be extended. Here, it is clear that, in a curved line obtained by connecting together a plurality of arcs, in case where gate positions are disposed at two points close to the end portions thereof, the curved line approaches a logarithmic curved line.
Also, on the contact central portion of a rolling surface, there may be formed a straight line portion which has a length 0.5-0.9 times the bus-direction effective contact length of the rolling surface and, on each of the two end portions of the rolling surface, there may be subjected a partial crowning consisting of a curved line portion which has a radius 50-125 times the present effective contact length.
In the above-mentioned roller bearing of the invention, it is preferable that a crowning profile providing the crowning quantity is one of a crowning profile and a partial crowning profile. The crowning profile may be composed of a combination of a plurality of arcs, a single arc or a combination of a straight line and arcs. The partial crowning profile may have a straight portion of a contact portion between the rolling surface of the rolling element and the first raceway surface of the first raceway and arcs at both ends of the contact portion.
Further, in the roller bearing of the invention, it is also preferable that the partial crowning profile satisfying following equations (3) and (4):
0.5xe2x89xa6Ls/Lexe2x89xa60.9xe2x80x83xe2x80x83(3)
xe2x80x8350xe2x89xa6R1/Lexe2x89xa6125xe2x80x83xe2x80x83(4)
where Ls=straight line portion length in the bus extending direction of the contact portion between the first raceway surface of the first raceway and the rolling surface of the rolling element; and R1=radius of the arc.
Furthermore, in the roller bearing of the invention, it is further preferable that the partial crowning profile satisfies following equations (5) and (6):
0.6xe2x89xa6Ls/Lexe2x89xa60.8xe2x80x83xe2x80x83(5)
75xe2x89xa6R1/Lexe2x89xa6100xe2x80x83xe2x80x83(6)
where Ls=straight line portion length in the bus extending direction of the contact portion between the first raceway surface of the first race and the rolling surface of the rolling element; and R1=radius of the arc.
The above-mentioned partial crowning profile further has a connecting arc which connects the straight line portion with the arc, the connecting arc satisfying following equation (7):
0.2R1xe2x89xa6R2xe2x89xa60.4R1xe2x80x83xe2x80x83(7)
where R2=radius of the connecting arc.
In the above-mentioned roller bearing of invention, it is further advantageous that the rolling element has one of a cylindrical-shaped rolling surface, a conical-shaped rolling surface, and a spherical-shaped rolling surface.